preprint numerics no. 1/2010 norwegian university of science and technology trondheim, norway Abstract. In this article, we construct a representation formula for stochastic B–series evaluated in a B–series. This formula is used to give for the first time the order conditions of implicit Taylor methods in terms of rooted trees. Finally, as an example we apply these order conditions to derive in...

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain...

Abstract: In this paper we investigate some stochastic models for tumor-immune systems. To describe these models, we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability in the equilibrium points, by constructing the Lyapunov exponent, depending on the parameters that describe the model. Stochastic stability was also proved ...

the effect of weak shear thickening and shear thinning on the stability of the taylor-couette flow is explored for a carreau-bird fluid in the narrow-gap limit. the galerkin projection method is used to derive a low-order dynamical system from the conservation of mass and momentum equations. in comparison with the newtonian system, the present equations include additional nonlinear coupling in ...

This work proposes a new numerical approach for dealing with fractional stochastic differential equations. In particular, novel three-point formula approximating the Riemann–Liouville integrator is established, and then it applied to generate approximate solutions Such derived use of generalized Taylor theorem coupled recent definition definite integral. Our compared solution generated by Euler...

A general framework is proposed for what we call the sensitivity derivative Monte Carlo (SDMC) solution of optimal control problems with a stochastic parameter. This method employs the residual in the firstorder Taylor series expansion of the cost functional in terms of the stochastic parameter rather than the cost functional itself. A rigorous estimate is derived for the variance of the residu...

In their classic paper, S. Orey and S.J. Taylor compute the Hausdorff dimension of the set of points at which the law of the iterated logarithm fails for Brownian motion. By introducing “fast sets”, we describe a converse to this problem for fractional Brownian motion. Our result is in the form of a limit theorem. From this, we can deduce refinements to the aforementioned dimension result of Or...

in this paper a modification of he's variational iteration method (vim) has been employed to solve dung and riccati equations. sometimes, it is not easy or even impossible, to obtain the first few iterations of vim, therefore, we suggest to approximate the integrand by using suitable expansions such as taylor or chebyshev expansions.

Abstract: In this paper we investigate some stochastic models for tumorimmune systems. To describe these models we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability in the equilibrium points, by constructing the Lyapunov exponent, depending on the parameters that describe the model. We have studied and analyzed a Kuznetso...